Alrite, let's all play nice and agree to disagree.
That being said, unless you physically remove the cochlea from the bird, chances are they will regenerate their hearing to at least some degree despite physical or chemical damage. Since birds have very acute hearing, removing it entirely may cause other social issues with the birds behavior wise.
I'm sure it "could" be done, but for research on pet animals/behavior that doesn't support human health or industry, I doubt IACAUC will pass the animal use protocols required for such experiments. Per their rules, you have to humanely kill things like fish with anesthesia, while thousands of wild fish get dragged up in nets, hooked by the mouth, and just tossed back in if they are undesired. With the state of funding at this time for research... even projects to save or improve the well being of humans are being cut. If all the money spent on fighting was spent on curing diarrhea or providing clean water, we would have fixed the number one killer of children in the world.
Perhaps the first experiment that can be asked is on behavior of why they crow. We know that the behavior is not started in the presence of other roosters, because roosters grown up in the absence of other roosters still crow. If a rooster was made deaf as a chick, we would be testing for if their ability to hear will determine if they will crow, while if we made a rooster deaf as an adult post crowing, we'd be seeing if "geriatric" hearing loss stops crowing.
Based on humans, being born deaf doesn't make them mute, and going deaf as an adult doesn't stop humans from talking. So I don't know how feasible this type of research would be, just based on previous work in the field.